In this note, we consider \(\mathcal {N}=2\)  SYM theories on compact, simply-connected four-manifolds \(X\)  with a \(T^2\) -action, generated by a Killing vector field with isolated fixed points. Many results have been obtained for this setup in the literature. Relying on these, it has been conjectured in [1]}, [2]} that any distribution of Nekrasov partition functions for either instantons or anti-instantons at each fixed point gives rise to the partition function of a supersymmetric theory. Taking \(S^4\)  as an example, by distributing instantons at both poles we obtain equivariant Donaldson-Witten theory [3]}, [4]}, [5]}, [6]}, counting anti-self-dual connections on \(S^4\) . Placing an instanton at one pole and an anti-instanton at the other pole instead gives Pestun's theory on \(S^4\)  [7]}, [8]}. Starting with anti-instantons at both poles gives again equivariant Donaldson-Witten, now counting self-dual connections.
